Problem: $\begin{aligned} &F(x)=5^{x} \\\\ &f(x)=F'(x) \end{aligned}$ $\int_{0}^{3} f(x)\,dx=$
$f$ is the derivative of $F$, which means $F$ is an antiderivative of $f$. Since we know the antiderivative of $f$, we can use the fundamental theorem of calculus: For every function $f$ and its antiderivative $F$, $\int_a^b f(x)\,dx=F(b)-F(a)$. $\begin{aligned} &\phantom{=}\int_{0}^{3} f(x)\,dx \\\\ &=F({3})-F({0}) \\\\ &=5^{{3}}-5^{{0}} \\\\ &=125-1 \\\\ &=124 \end{aligned}$ In conclusion, $\int_{0}^{3} f(x)\,dx=124$